The only use case I can think where matlab beats Python or Julia is when one has a lot of legacy code. It's funny that you mention documentation, the amount of documentation found around Python is typically much better than matlab. Matlab toolboxes are really hit and miss, some are very good, but there are some really crappy ones. If you actually need to include more traditional programming features matlab becomes a hot mess. Looking at matlab GUI code gives me nightmares for weeks....
I would not wish Matlab GUI programming on my worst enemy.
I disagree with your assertion that documentation for Python is typically much better. Take a randomly chosen function I regularly use: "pwelch"
Maybe my bias is showing, but I find the Matlab documentation to be superior. However, that is nothing compared the quality of the IDE which is critical when doing scientific compute. When I was re-evaluating our simulation environment at work, we looked at PyCharm. The plotting capabilities alone made it easy to stick with Matlab, even at the orders of magnitude higher cost.
N.B. This is my experience in an Optical Communications R&D environment.
Funny I'm in optical comms as well, chances are we know each other. I never used "pwelch" though. But I concur my statement on documentation was too strong, I guess it depends quite a bit.
Regarding IDE, I guess we tend to put priorities on different things. I find pycharm's (pro edition) git Integration, debugging, refactoring and profiling vastly superior. I plot using regular qt windows and I agree that for interactive plots where one wants to look at points etc, matlab has the edge, for publication ready plots matplotlib beats matlab hands down though (although the API is quite verbose, proplotlib is a wrapper that makes things more convenient IMO).
Anyway I think we have different priorities in what we are looking for. We use Python for labautomation and the matlab instrumentation toolbox is a buggy mess, our measurement times decreased by a factor of 5-10 when we switched from matlab.
Regarding cost, we are a university so matlab and python have equal costs. I do know of colleagues at industry labs where matlab cost was a factor though.
